The annual meeting of the International Monetary Fund was a dismal affair. Ministers arrived in Washington with the global economy drifting towards a currency war and they left town having done nothing to stop hostilities breaking out. The co-operation that was so evident in October 2008, when the banks were falling like ninepins, was nowhere to be seen.

It seems that policymakers cope well with a crisis but find it hard to agree once the immediate threat has gone away. The brutal reality of this year's gathering was that structural flaws in the system of global economic governance mean little can be done to resolve the dispute between the US and China.

It has taken the US a full 66 years to get it, but Keynes was right. When there are imbalances in the world economy, both creditor and debtor nations need to adjust their policies. The system the Americans insisted upon at the Bretton Woods conference in 1944 put all the burden on the debtor countries. Surplus countries are not obliged to do anything. This, as Keynes realised, was a recipe for trouble and so it has proved.

The imbalances in the global economy were at the root of the financial crisis in 2007, because the surpluses from China (and other countries running trade deficits) had to find a home. They were accommodated by the west's financial markets, which used the hot money to fund asset-price booms, developing a range of esoteric investment vehicles in the process.

The recession of 2008-09 led to a narrowing of the imbalances, but it was only temporary. It is clear what needs to happen. Debtor nations have to wean themselves off debt-financed consumption; they have to export more and import less. Creditor nations need to do the opposite: they need to boost domestic demand, thereby soaking up the exports from the debtor nations.

That's the theory. In practice, it is proving impossible to finesse this rebalancing, because the big creditor nations – China and Germany – are refusing to take the necessary measures to run down their trade surpluses. The international monetary system is designed to force countries running trade deficits to deflate their economies in order to get imports and exports back into balance.

Harry Dexter White, the chief US negotiator (and, as it later transpired, a Soviet spy), said at Bretton Woods that this was the way it had to be.

Special pleading

It's not hard to see why the Roosevelt administration took this view. The US was a creditor nation of enormous proportions and saw Keynes's arguments as special pleading on the part of Britain, desperately trying to stave off the reality of economic decline. Roosevelt was keen to see the British empire dismantled and was determined to take a tough line in the Bretton Woods talks. And, since the US accounted for about half the global economy at the end of the second world war, it called the shots.

The upshot was the asymmetric model that has been the template for adjustment ever since. When Britain ran into balance of payments problems in 1949 and 1967, the remedy was devaluation accompanied by a strong dose of domestic austerity. The same philosophy lay behind the structural adjustment programmes imposed on developing countries.

Back in 1944, the Americans did not envisage that they would one day be the world's biggest debtor nation. For years they have been able to stave off the consequences of running a large trade deficit by printing more dollars. That's something you can get away with if you are the world's premier reserve currency, but at a price. The imbalances grew bigger and bigger until they threatened the stability of the world economy.

The Americans are now able to see the downside of the system they themselves created: what do you do when a creditor nation tells you to push off, as the Chinese have done in the past week after pressure from Washington to revalue the yuan? The answer, as Tim Geithner, the US treasury secretary, has discovered, is that you plead and you cajole and you threaten, but you have little traction unless you are prepared to "go nuclear" and impose trade barriers.

The fear is that the US – beset by high unemployment and a crippled housing market – is getting ever closer to the point where it loses patience with China and goes down the protectionist route.

Friday's employment figures were again grim – jobs are still being shed 18 months into a recovery, a huge social and political headache for a country that has a less generous welfare system than that in most European countries. From the Tea Party activists on the right to the unions on the left, there is a strong feeling that free trade is bad for America.

The idea that a revaluation of the yuan is a magic bullet for the US economy is wrong. After two decades of hollowing out, the US manufacturing base is neither strong enough nor big enough to respond immediately to the boost provided by a shift in exchange rates.

Sudden shift

But it is also clear that China's policy of building up ever-larger trade surpluses is incompatible with global economic stability. Beijing's line last week was that a sudden shift in its economic model would cause economic and social upheaval, something the ruling Communist party wants to avoid at all costs.

The difficulty, though, is that China's surpluses have to be matched by deficits elsewhere. In the US, that means that either the private sector can run up debts or the government has to be prepared to tolerate big budget deficits. This is not an appetising choice.

So what happens now? One solution would be for the Chinese to agree a medium-term plan with the Americans to revalue the yuan, providing a five- or 10-year period to make the adjustment to a less export-dependent economy. The G20 was established with the aim of brokering precisely this sort of deal.

Sadly, after a good start, the G20 is proving disappointingly ineffective. Far too many countries and international organisations have found a way of gate-crashing the meetings, turning them into a G30. That has meant plenty of talk but little action. What's more, the departure from the international scene of Gordon Brown means there is nobody driving the process forward.

As a result, the unity of purpose that marked late 2008 and early 2009 is rapidly ebbing. This weekend's meeting of the IMF pledged to work towards a "more balanced pattern of global growth, recognising the responsibilities of surplus and deficit countries", but the empty rhetoric failed to disguise the total lack of progress.

Indeed, the Americans are probably closer to pushing the nuclear button than they were before the weekend. The jobs figures highlighted the fragility of the economy, while the IMF meeting highlighted the impotence of the multilateral system. If, as seems apparent, the world can only pull together in a crisis, America and China between them may be about to provide one.